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Topology

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Closures of Sets of Real Numbers

TOPO-EEL9JB

Consider the real numbers $\mathbb{R}$ with their usual (metric) topology, and the subset:

$$A=\{\frac{1}{n} : n = 1,2,3,...\}$$

Which of the following is the closure of $A$?

A

$A$

B

$\{0\}$

C

$[0,1)$

D

$[0,1]$

E

$A\cup\{ 0\}$